重难点13极化恒等式与等和（高）线定理四大题型（原卷版）_11.4-2_2026-11-04

      
      
重难点13 极化恒等式与等和（高）线定理【四大题型】

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3
2
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1
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3
2;t&    )
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2
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/8Y;𝐴𝐸/ĜS+1𝐶𝐷æpY𝐹g
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2 = 𝑎2 +2𝑎⋅𝑏+ 𝑏2; 𝑎−𝑏
2 = 𝑎2−2𝑎⋅𝑏+
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1
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Y;𝐵𝐷æ𝐴𝐸p𝑂.
  
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1
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1
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2 = 𝑎2 +2𝑎⋅𝑏+
𝑏
2W②(𝑎−𝑏)
2 = 𝑎2−2𝑎⋅𝑏+ 𝑏
2.X①-②_(𝑎+ 𝑏)
2−(𝑎−𝑏)
2 = 4𝑎⋅𝑏⇔𝑎⋅𝑏= (𝑎+𝑏)
2−(𝑎−𝑏)
2
4
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7>~“G”/Ħħ.†‡ß
}/DEF𝐴𝐵𝐶𝐷8;𝐵𝐷= 8,𝐴𝐵⋅𝐴𝐷= 48;𝐸~𝐵𝐷8Y.
(1)Œcos∠𝐵𝐴𝐷=
12
13;# △𝐴𝐵𝐷/5>W
(2)Œ2𝐴𝐸= 𝐸𝐶;#𝐶𝐵⋅𝐶𝐷/$W
(3)Œ𝑃~45𝐴𝐵𝐶𝐷—‰Y;#𝑃𝐴⋅𝑃𝐵+ 𝑃𝐷/%Ú$.